Resonance-shifting luminescent solar concentrators

ABSTRACT

An optical system and method to overcome luminescent solar concentrator inefficiencies by resonance-shifting, in which sharply directed emission from a bi-layer cavity into a glass substrate returns to interact with the cavity off-resonance at each subsequent reflection, significantly reducing reabsorption loss en route to the edges. In one embodiment, the system comprises a luminescent solar concentrator comprising a transparent substrate, a luminescent film having a variable thickness; and a low refractive index layer disposed between the transparent substrate and the luminescent film.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. application Ser.No. 13/199,323 filed Aug. 26, 2011, reference of which is incorporatedin its entirety.

STATEMENT OF GOVERNMENT INTEREST

The United States Government claims certain rights in this inventionpursuant to Contract No. DE-AC02-06CH11357 between the U.S. Departmentof Energy and UChicago Argonne, LLC, representing Argonne NationalLaboratory.

FIELD OF THE INVENTION

The present invention relates generally to solar concentrators. Moreparticularly, the present invention relates to systems and methods forimproving the efficiency of luminescent solar concentrators.

BACKGROUND

The modernization and urbanization of developing countries places anincreasing demand on supplies of fossil fuels and the use of such fuelsplaces an increasing burden on the environment. As market demand drivesfuel prices upward and as increased consumption acceleratesenvironmental pollution, alternative energy sources become moreeconomically feasible and socially popular. Among the variousalternative energy sources, solar energy is one of the most promisingdue to the endless supply of free energy from the sun. One method ofharnessing the sun's energy is through optical solar concentration.

Solar concentration is used in combination with traditional photovoltaiccells to reduce the area of cells necessary to generate a given amountof electrical energy. In particular, sunlight shining on a solarconcentrator is optically concentrated and transmitted to a solar cell.Through optical concentration, or geometric gain, a smaller photovoltaiccell can be used to generate a given amount of electrical energy. Byreducing the photovoltaic cell area necessary to generate a given amountof electrical energy, optical concentration reduces the cost of energyproduction.

There are two distinct approaches to solar concentration. One approachuses lenses or mirrors and tracks the sun throughout the day. Thistracking approach can produce very high concentration (e.g. greater than500 suns) but requires tracking to within 0.1 degree and, therefore, isexpensive and susceptible to tracking errors that may reduceperformance. Another approach does not track the sun. One example ofthis non-tracking approach uses fixed lenses and mirrors, which producesrelatively low concentration (e.g. less than 5 suns). Another example isthe luminescent solar concentrator (LSC).

Optical solar concentration provides a realistic, near-term prospect forleveraging the cost and expanding the generation capacity of today'sestablished solar cell technologies. The maximum concentration ratio(CR) obtainable using linear geometric optical systems involving lenses,mirrors, or diffractive optics, is fundamentally limited by theacceptance angle (θ_(acc)) of the system and the refractive index(n_(out)) at its output aperture through the well-known sine law,CR≦(n_(out)/sin θ_(acc))². Maintaining high concentration (CR>100)throughout the day thus demands that these concentrators track the sunwith high precision, which drives up both capital and maintenance costsof the overall system.

LSCs were developed in the 1970s and have a high fundamentalconcentration (e.g. greater than 100 suns). LSCs were introduced as analternative, non-tracking approach that preserves, at least inprinciple, the potential for high concentration. However, technicalissues have limited the utility of LSCs to date. LSCs provide a simplemeans to concentrate sunlight without tracking the sun. These devicesoperate by absorbing light and then re-emitting it at lower frequency,typically into the confined modes of a transparent slab, where it istransported toward photovoltaic cells attached to the edges. In thethermodynamic limit, concentration ratio exceeding the equivalent of 100suns is possible, however, in actual LSCs, optical propagation loss duemostly to reabsorption limits the concentration ratio to approximately10.

In contrast to their ‘passive’ geometric optical counterparts, LSCsactively shift the optical frequency by absorbing sunlight andre-emitting it with a finite Stoke's shift into the confined opticalmodes of, e.g. a transparent slab, where it is trapped by total internalreflection and absorbed by photovoltaic cells attached to the edges. Thelimiting concentration ratio for an LSC follows from thermodynamicconsiderations and is exponential in the Stoke's shift according toCR_(lim)≈(e_(em) ³/e_(abs) ³)exp [(e_(abs)−e_(em))/k_(b)T], wheree_(abs) and e_(em) are the absorbed and emitted photon energies,respectively. This theoretical maximum exceeds the equivalent of 100suns for most emitters employed in LSCs to date, yet the value realizedin practice is more than an order of magnitude lower, typically in therange 2<CR<10, which remains too low to provide any economic benefit inreducing the cost of photovoltaic power. The following provides a newapproach to LSC optical design that enables a doubling or more in CR forany type of emitter, thereby improving the prospect of low-cost,high-performance luminescent concentration.

SUMMARY

Various embodiments of the present invention comprise an all-opticalsystem and method to overcome LSC problems by ‘resonance-shifting’, inwhich sharply directed emission from a bi-layer cavity into the glasssubstrate returns to interact with the cavity off-resonance at eachsubsequent bounce, significantly reducing reabsorption loss en route tothe edges. Near-lossless propagation is demonstrated for severaldifferent chromophores that ultimately enables a more than two-foldincrease in concentration ratio over that of the correspondingconventional LSC.

In one embodiment, a luminescent solar concentrator is provided,comprising a transparent substrate, a luminescent film having a variablethickness, and a low refractive index layer disposed between thetransparent substrate and the luminescent film. In another embodiment, amethod for increasing the efficiency of a luminescent solar concentratoris provided. In this embodiment, the efficiency is increased byproviding a low refractive index layer to a surface of the transparentsubstrate and providing a luminescent film of laterally varyingthickness to a surface of the a low refractive index layer, such thatthe low refractive index layer is disposed between the transparentsubstrate and the luminescent film. In another embodiment, a method ofdirecting light is provided. In this embodiment, light is directed byabsorbing a light at a first location in a luminescent film, emittingthe light through a low refractive index layer into a transparentsubstrate, the emitted light evanescently coupled into the transparentsubstrate, reflecting the light from a bottom boundary of thetransparent substrate, and reflecting the light from a second locationin the luminescent film laterally displaced from the first location,wherein the light exhibits non-resonant near-unity reflectivity.

These and other features of the invention, together with theorganization and manner of operation thereof, will become apparent fromthe following detailed description when taken in conjunction with theaccompanying drawings, wherein like elements have like numeralsthroughout the several drawings described below.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof necessary fee.

FIGS. 1 a and 1 b illustrate the resonance-shifting concept applied to aluminescent solar concentrator; FIG. 1 a is an illustration of theresonance-shifting concept, where a thin luminescent film layer isseparated from a glass substrate by a low refractive index(n_(low)˜1.14) layer; FIG. 1 b illustrates the same sequence as FIG. 1a, but is from the perspective of internal substrate angle, where thereflectivity dip due to reabsorption loss shifts to higher angle for thethicker luminescent film, with near-unity reflectivity at the originalemission resonance.

FIGS. 2 a and 2 b depict the emitter and bi-layer cavitycharacteristics; FIG. 2 a depicts the thin-film absorption (dash-dotlines) and emission spectra (solid lines) of three luminescent materials(green-emitting polymer poly(9,9-di-n-octylfluorene-alt-benzothiadiazole) (“F8BT”) and twoperylene-based Lumogen F-series dyes (“L170” and “L305” respectively)),illustrating various self-absorption overlaps (photoluminescence spectrafor each material were collected normal to the film surface and scaledto the absorption peak); FIG. 2 b depicts emission and reflectivitypatterns measured for a bi-layer F8BT cavity as a function of angle inthe glass substrate where the plots with circles and the plots withsquares (right-hand scale) indicate reflectivity of the bare cavityobtained at λ=543 nm whereas the emission (left-hand scale) was detectedthrough a λ=550 nm bandpass filter. The bare cavity emission peaks(bowtie-shaped symbols) correspond to the resonant reflectivity dips,where the slight mismatch in peak angle and broadening of emissionrelative to the reflectivity are due to the center wavelength differenceand bandwidth of the filter, respectively. Evaporating 30 nm of Alq₃onto the F8BT increases the cavity phase and shifts the emission peaksto higher angle (“x”-denoted plot), off-resonance with the barereflectivity as indicated by the dashed arrows. Solid lines indicatefits to a transfer matrix-based model as discussed in the text.

FIGS. 3 a-c illustrate resonance-shifting with F8BT. FIG. 3 a is aschematic of the experimental geometry, where a Si photodiode,index-matched to the sample edge, records the luminescence intensitygenerated by laser excitation as a function of distance, x. Thecross-hatched vertical stripe indicates a resonance-shifted region ofthe sample with increased cavity thickness. Photographs 1, 2, and 3 showthe progression of directional emission rings from the F8BT cavity ofFIG. 2 b as the excitation spot approaches the resonance-shifted stripeindicated by the arrow. Ring components that cross from one region toanother disappear as they become non-resonant. FIG. 3 b depicts internaloptical quantum efficiency measured as in (a) for complementary F8BTcavities, showing an increase in edge emission upon crossing over theresonance-shifted region of each. The LSC control is identical to thecavities except that it has no low-n spacer layer. Estimating thepropagation efficiency from these measurements (right-hand scale) showsthat resonance-shifted emission propagates with near-zero loss. FIG. 3 cillustrates the progression of edge emission from the RS+ sample (seethe inset of FIG. b) viewed on a white card as the excitation point ismoved farther from the edge. Near the edge (x=0.5 and 2.5 mm), emissionmoves from one side to another as shown in the diagram. Crossing fromx=29 mm into the resonance-shifted stripe at x=31 mm leads to therecovery of additional green emission indicated by the white arrows dueto reduced reabsorption loss.

FIGS. 4 a-d depict an analysis of resonance-shifting with L305. FIG. 4 adepicts internal optical quantum efficiency (IQE) measured for the L305control LSC and complementary resonance-shifted cavities. The intensitydecrease in the RS+ stripe is due to a decreased emission quantum yieldinto the substrate; it is regained in the large RS− increase.Propagation efficiency is deconvolved from the changes in emissionquantum yield and displayed on the right hand scale. FIG. 4 b depictsedge-emission spectra, collected through the port of an integratingsphere as shown in the inset. The spectra are normalized to one anotherat long wavelengths (λ>740 nm) to calculate the self-absorption ratiosshown in the inset. The resonance-shifted spectrum (denoted 33 mm)recovers high-energy emission that would otherwise be lost toreabsorption, as in the trace denoted 30 mm. FIGS. 4 c-d depictsimulated IQE and emission spectra corresponding to the measurements inFIGS. 4 a and 4 b as calculated using the structure, optical constantsand photoluminescence spectrum of L305.

FIG. 5 a illustrates measurement of concentrator performance underoperational conditions, in which the area of uniform illumination(geometric gain) is varied as shown. The photodiode is covered (notshown) to prevent it from receiving direct illumination. Theresonance-shifting pattern is a 6-level staircase with 2 mm wide stepsas shown. FIG. 5 b depicts edge detected luminescence power collectedfor an F8BT control LSC and RSLSC. The lower panel shows the absorptionmeasured along the center of each concentrator. FIG. 5 c depicts resultsof the same experiment performed with L305-based devices. The absorptionof each (lower panel) is nearly identical and clearly shows thestep-like thickness variation. FIG. 5 d depicts ratio of theedge-detected RSLSC power to that of the corresponding LSC control forthe three emitters on borosilicate and high-index SF10 glass substrates,with d_(low)=230 nm in each case and base layer thicknesses of 267 nmand 150 nm for the F8BT and Lumogen devices, respectively. An increasingratio for each with geometric gain indicates reduced propagation loss inthe RSLSC.

FIGS. 6 a-b depicts simulation of concentrator performance. FIG. 6 adepicts and extension of the simulations in FIGS. 4 c and 4 d to predictthe power emitted from one edge of an L305-based RSLSC and LSC controlunder uniform area illumination as in FIG. 5 c. Both the magnitude ofthe RSLSC enhancement and the trend in power ratio are similar to thatobserved experimentally in FIG. 5 d. FIG. 6 b depicts the samesimulation accounting for emission from all four edges and extended tolarger geometric gain. Here, the L305 photoluminescence quantum yield isset to 98% and the concentration ratio is calculated explicitly, clearlyillustrating the benefit of reduced loss obtained by resonance-shifting.

FIG. 7 a illustrates emission outcoupling from the bi-layer cavity via ahalf-ball lens, showing the highly direction rings of emission projectedonto a screen. FIG. 7 b depicts typical emission rings from an F8BTcavity similar to that in FIG. 3 b.

FIGS. 8 a-d illustrate reflectivity and optical field intensity profilescalculated from fits to the data of the F8BT cavity in FIG. 3 b. FIGS. 8(a) and (c) illustrate the TE and TM reflectivity profiles,respectively. The reabsorption loss, given by 1−R, is significantlylower off-resonance in both polarizations for the cavity than for thesame F8BT film on glass. FIGS. 8 (c) and (d) show the optical fieldintensity profile calculated for the structure at the (off-resonance)angles indicated by the dashed arrows in (a) and (c). The fieldintensity is much lower in the F8BT film off resonance than it is forthe control F8BT film on glass, which is the physical basis for thereduced reabsorption in the case of the cavities.

FIG. 9 illustrates the geometry and variable definitions used in themodel calculations.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented here. It will be readily understood that the aspects of thepresent disclosure, as generally described herein, and illustrated inthe figures, can be arranged, substituted, combined, and designed in awide variety of different configurations, all of which are explicitlycontemplated and made part of this disclosure.

Concentration ratio is defined as the ratio of output to input radiantflux, and in the case of LSCs 10, it is factored according toCR=Gη_(opt), where the geometric gain G=A_(out)/A_(in) is the ratio ofoutput to input aperture areas and η_(opt)=P_(out)/P_(in) is theefficiency of power transfer from sunlight incident on the concentrator(Pin) to that of the luminescence at its output (Pout). The opticalefficiency is often approximated as a product,η_(opt)≈η_(abs)η_(Stokes)η_(em)η_(prop) (G), which depends on theabsorbed fraction of the solar spectrum (ηabs), the fractional photonenergy loss in down-conversion (ηStokes), and the probability ofre-emission into confined modes (ηem). The final factor, ηprop, accountsfor all propagation-related losses due to reabsorption and scatteringand hence, in contrast to the other losses, is a naturally decreasingfunction of G. It is this functional dependence that is ultimatelyresponsible for the low CR achieved in practice since, if ηprop wereconstant, G could simply be increased to compensate for the otherlosses.

The falloff of ηprop with increasing G is predominantly due toself-absorption by the luminescent material, in which emitted photonsare reabsorbed by the tail of the absorption spectrum and thensubsequently lost due to non-radiative decay or secondary re-emissionout of the waveguide. One strategy for combating this problem is tominimize the overlap between absorption and emission spectra byincreasing the Stoke's shift, either via cascaded energy transfer or theuse of emitters with intrinsically large shifts, such as rare-earth ionsand phosphorescent organic molecules. This approach has recently showngreat promise for LSCs 10 based on organic thin films, however, it isnot easily applicable to other emitters such as colloidal quantum dotsdue to their large self-absorption overlap, and more fundamentally, itdoes not improve CR relative to the thermodynamic limit since CRlim alsogrows with increasing Stoke's shift, as noted above. Alternatively,wavelength-selective filters have been used to reduce out-coupling ofphotons re-emitted within the critical angle, but this can adverselyaffect the in-coupling of direct and diffuse sunlight at wide angles andit ultimately does not resolve the non-radiative component ofreabsorption loss.

Resonance-shifting addresses the reabsorption problem differently inthat it relies on emission from optical resonances that change withposition across the concentrator, such that subsequent interactions withthe emissive region are non-resonant with greatly diminishedreabsorption. FIG. 1 a illustrates a simple implementation of thisconcept, in which a thin film of the luminescent material, typically amicron or less in thickness, d_(em), is separated from a glass or othertransparent substrate 12 by a layer with low refractive index (herenlow˜1.14, though can range from about 1.1 to about 1.2) and thickness,d_(low). This structure constitutes an evanescently coupled bi-layercavity, in which slab waveguide modes supported by the emissivethin-film become leaky (into the substrate 12 of similar refractiveindex) when the low refractive index (low-n) layer thickness is on theorder of half the emitted wavelength. Emission into these modes isfavored on account of their increased photonic density of states andhence a large fraction (typically 60-90%) of the thin-filmphotoluminescence can be coupled into the glass substrate 12 at sharplydefined angles (see FIG. 1 b) corresponding to each discrete mode.

These modes, by nature, cannot propagate in air and hence thedirectional emission undergoes total internal reflection at the opposingglass/air interface and returns to the emitter/low-n bi-layer laterallydisplaced by roughly twice the substrate 12 thickness. If the waveguidethickness (e.g. the luminescent film 16) were to remain unchanged fromthe original emitting position, the emitted light would be resonantlycoupled back into the slab waveguide and reabsorption would beintensified. However, if the original emission returns to find adifferent waveguide thickness, then it will be non-resonant with the newcavity modes and the reflectivity, R, may consequently approach unity.Since no light is transmitted under conditions of total internalreflection, reabsorption loss, given by the balance 1−R, is drasticallyreduced.

From a physical standpoint, the decrease in reabsorption is due toreduced overlap of the optical field intensity profile (|E|2) with theluminescent film 16, as illustrated in FIG. 1 a. Off resonance, theoptical fields decay evanescently from the glass substrate 12 throughthe lossless low-n layer such that only the tail of the intensityprofile samples the luminescent film 16. By contrast, the intensityoverlap, and hence reabsorption, is much larger in conventionalthin-film LSCs 10 (e.g. luminescent film 16 on a glass substrate 12)since the optical fields do not decay before reaching the emissivelayer. This point is further illustrated below through calculation ofthe field profiles (equations 1-4).

The scheme shown in FIG. 1 works bi-directionally, that is, emissionfrom the left-hand side is non-resonant on the right-hand side and viceversa. It is also broadband since the dispersion of each mode ensuresthat its propagation constant (i.e. resonant angle) changes withwavelength. Hence, light at each emission wavelength couples into thesubstrate 12 at its own unique set of angles and then propagatesindependently through the concentrator; in short, different wavelengthsare not subject to the resonances of one another.

The goal in designing a resonance-shifting luminescent concentrator(RSLSC) is thus to vary the thickness of the luminescent film 16 acrossthe surface of the concentrator such that resonant emission from anygiven location does not re-encounter that same resonance in reflectivityelsewhere before reaching the RSLSC edges. The required thicknessvariation 18—typically a few tens of nanometers over a lateral distanceof approximately twice the substrate 12 thickness (i.e. the returnlength between bounces)—is determined by the resonance width, which inturn depends on modal coupling to the substrate 12 through dlow as wellas the extinction coefficient of the emissive layer.

The RSLSC strategy was tested for three different luminescent materials,namely, the green-emitting polymerpoly(9,9-di-n-octylfluorene-alt-benzothiadiazole) (F8BT) and twoperylene-based Lumogen F-series dyes (denoted here as L170 and L305)that are commercially available from BASF Corporation and are routinelyused in LSCs 10. FIG. 2 a presents the thin-film absorption and emissionspectra of each material, which feature varying degrees ofself-absorption overlap and photoluminescent quantum yields, measured inan integrating sphere, that range from φPL=0.75±0.04 for F8BT to0.44±0.03 and 0.03±0.01 for L170 and L305, respectively. φPL is nearunity for the Lumogen dyes dispersed in a host matrix, however, testingcapabilities were restricted to thermal evaporation of neat films wherethe luminescence is self-quenched. Nevertheless, this collection ofemitters, together with both standard borosilicate and high-index SF10glass substrates 12, provides a broad test-bed from which to assess theeffectiveness of the RSLSC approach. As explained in further detailbelow, while these three emitters have been tested, other emitters, suchas colloidal quantum dots and organic dyes used in conventionalluminescent concentrators, may be used to achieve similar results.

The angular emission pattern of an F8BT/low-n bi-layer, fabricated aspreviously by spin-coating on a glass microscope slide (1 mm thick) andout-coupled using a hemispherical prism, is shown in FIG. 2 b by theplot with bowtie symbols. The cavity exhibits highly directionalemission, visible as rings by eye (FIG. 7) that consist of two dominantpeaks at angles (in glass) of θ˜49° and θ˜72° that correspond totransverse electric and magnetic TE1 and TM0 modes, respectively. Theangularly directed emission of F8BT cavities is easily seen by eye whenout-coupled with a hemispherical prism as shown in FIG. 7 a. Aphotograph showing the typical emission ring pattern observed from anF8BT cavity is shown in FIG. 7 b, where the color change from the innerto outer edge of each ring reflects the modal dispersion in thewaveguide.

The transverse electric and magnetic TE1 and TM0 modes are also evidentin the prism-coupled angular reflectivity spectra (FIG. 2 b, plots withcircles and plots with squares, right-hand axis), where the smallmismatch in mode position between emission and reflectivity is due todispersion since they are measured at slightly different wavelengths,with reflectivity recorded at λ=543 nm and emission collected through aλ=550 nm bandpass filter (Δλ=10 nm). As shown by the solid lines, bothemission and reflectivity data are well-reproduced by standard transfermatrix models, with optical constant inputs and dem=267±3 nm anddlow=230±8 nm determined from spectroscopic ellipsometry.

In contrast to the ‘bare’ F8BT cavity, the emission pattern denoted by“x” symbols in FIG. 2 b has been shifted to higher angle by thermallyevaporating 30 nm of the organic semiconductor tris (8-hydroxyquinoline)aluminum (Alq3) onto the F8BT surface. The Alq3 layer is transparent tothe λ=473 nm excitation wavelength and has a similar refractive index toF8BT, thus it serves only to increase the cavity phase and shift theemission peaks away from the bare cavity reflectivity resonances asshown by the dashed arrows. A closer examination of the reflectivityfitting (provided below) shows that loss due to reabsorption (e.g. 1−R)in the off-resonance locations averages over an order of magnitude lessthan it would be for conventional LSCs 10 (e.g. dlow=0 nm) with the sameF8BT film.

FIG. 3 presents a more visually striking demonstration ofresonance-shifting and its capability to reduce loss. The experimentalsetup is shown in the upper-left panel of FIG. 3 a, where a Siphotodiode 20 is index-matched to one edge of the substrate 12 and alaser excitation spot is scanned along the middle of the sample. Theupper-right photograph (panel 1) shows the result of exciting the bareF8BT cavity, where several emission rings surrounding the centralexcitation point are visible. These rings correspond to reflections ofthe directional emission that are resonantly reabsorbed and re-emitted,or scattered out of the glass upon each subsequent interaction with thecavity. In the photograph below (panel 2), the excitation spot istranslated adjacent to a 2 mm wide, 30 nm thick Alq3-resonance-shiftedstripe indicated by the white arrow. Ring components within the stripeare no longer visible since they are non-resonant and remain trappedwithin the glass. Similarly, in panel 3, when exciting at the center ofthe stripe, ring components outside the stripe disappear since they arenow non-resonant with the bare cavity.

FIG. 3 b shows the internal optical quantum efficiency (IQE), orfraction of photons absorbed at the excitation spot that are re-emittedand detected by the photodiode 20. A clear increase in edge emission isobserved when the excitation point crosses over the resonance-shiftedstripe (RS+). However, to rigorously ascribe this change to reducedpropagation loss, as opposed to a change in quantum yield of the cavityemission into the substrate 12, the inverse configuration (RS−) as shownin the inset was tested, where the ‘stripe’ region is left bare and 30nm of Alq3 is deposited elsewhere. The similar result evident in the RS−case confirms that the increase is due to reduced propagation loss.

Combining the IQE data of both RS+ and RS− enables the resonance-shiftedpropagation loss to be deconvolved from the changes in substrate-coupledemission quantum yield that accompany the variation 18 in cavitythickness and thus calculate a single, ‘average’ propagation efficiency,ηprop(x), which is further explained below. According to the right-handscale of FIG. 3 b, after propagating 25 mm, emission in the LSC 10control is reduced to ˜85% of its initial intensity, whereas in theresonance-shifted case, it recovers to near 100%, illustrating thecapability for low loss propagation.

FIG. 3 c shows the progression of emission emanating from the edge ofRS+ and projected onto a white card. Exciting adjacent to the edge(x=0.5 mm), the directional emission exits to the right-hand sidewithout undergoing any bounces, as depicted in the initial illustration.At x=2.5 mm, the emission undergoes a single bounce and now exits to theleft-hand side. As the excitation point moves far from the edge (x=29mm), the emission intensity out each side becomes similar since the TEand TM modes are emitted at different angles and thus do not remain instep with one another. Upon exciting the resonance-shifted stripe (x=31mm), additional green emission appear, indicated by the white arrows,which contributes to the intensity increase recorded by the photodiode20 in FIG. 3 b. Since the high energy, green component of F8BT emissionis most strongly attenuated by the absorption tail, it is the dominantcomponent recovered when loss is reduced by resonance-shifting.

Although F8BT provides a qualitatively useful visual demonstration, amore in-depth analysis is complicated by the natural, uncontrolledthickness variation 18 inherent in the spin-coated films. Rigorousexperimental and modeling analysis instead focused on more uniformdevices fabricated by thermally evaporating films of L170 and L305. FIG.4 shows the results obtained for the L305 control, RS+, and RS−structures, where dlow=230±8 nm and dem=150±4 nm, with a 30 nm thicknesschange in the resonance-shifted stripe. FIG. 4 a illustrates an IQEdecrease in the RS+ stripe and a significantly larger magnitude IQEincrease in the RS− stripe. This indicates a significant change in theyield of substrate-coupled emission between the two cavity thicknesses,with the dem=150 nm cavity emitting more efficiently into the glass thanthe dem=180 nm cavity. This change is more significant than for F8BT inFIG. 3 b primarily because the resonance shift in the L305 cavity isaccompanied by the onset/disappearance of an available TE0 mode over alarge portion of the L305 photoluminescence spectrum. Nevertheless, whenpropagation efficiency is deconvolved from the changes in emissionquantum yield, the resonance-shifted stripe recovers to 96% of itsstarting value, whereas the control LSC 10 drops to 78% (FIG. 4 a,right-hand axis), representing an approximately 5-fold reduction inloss.

FIG. 4 b shows the edge emission spectra of the L305 complementarydevices collected through the port of an integrating sphere as shown inthe inset diagram. The spectra are strongly modified from thephotoluminescence in FIG. 2 a and all exhibit a discontinuous ‘kink’ atλ˜720 nm that corresponds to onset of the TE0 mode and increasedemission at longer wavelengths. Self-absorption (SA) ratio, plotted inthe inset, is determined by normalizing the spectra to one another atlong wavelengths (λ>740 nm) where reabsorption is negligible and thencalculating the spectrally integrated intensity decrease relative to theinitial spectrum obtained exciting at x=2 mm from the edge. The SA ratiothus quantifies the red-shift in luminescence spectrum that typicallyoccurs as light propagates through an LSC 10, with high SA ratios (i.e.near unity) indicating little reabsorption and vice versa. The inset ofFIG. 4 b illustrates an increase in SA ratio for both RS+ and RS−resonance-shifted stripes, due mostly to the recovery of stronglyabsorbed, high-energy spectral components as evident from the differencein x=30 mm and x=33 mm spectra. The data and trends obtained for theL170 cavity are similar to those in FIGS. 4 a and 4 b, as are those forL170 and F8BT cavities on high-index SF10 substrates 12.

FIGS. 4 c and 4 d present simulated optical IQE and edge emissionspectra that correspond to the measurements in FIGS. 4 a and 4 b.Briefly, the simulations involve calculating the cavity emission andangular reflectivity profiles at each wavelength and then integratingover all propagation paths, accounting for reflectivity loss at eachbounce en route to the substrate edge; details are provided below.Overall, the simulations are in reasonable qualitative agreement withthe data, reproducing the TE0 onset ‘kink’ and high-energy emissionrecovery in the spectra of FIG. 4 b as well as the optical IQE magnitudeand trends in FIG. 4 a. The discrepancy in sign change of the RS+ stripebetween FIGS. 4 a and 4 c implies that the predicted cavity-modifiedemission quantum yields are not fully accurate, though the trend iscorrect insofar as the RS− increase exceeds that of RS+. Additionally,the simulations predict greater optical loss for the un-shifted regionsof each cavity as compared to the control LSC 10, which is intuitivelyexpected since emission in the un-shifted regions undergoes resonantloss at each bounce. Indeed, it is not currently clear why theun-shifted portions of RS+ and RS− decrease at nearly the same rate asthe control in the data of FIG. 4 a. Secondary re-emission events notaccounted for in the model and slight deviations in the substrate 12surface planarity that naturally return light off-resonance maycontribute to this discrepancy.

These results demonstrate the potential of resonance-shifting to reducepropagation loss, but whether this can ultimately be harnessed to netbenefit in an actual RSLSC consisting of many such shifts is mostdirectly addressed by measurement under operating conditions. This isshown schematically in FIG. 5 a, where a fully patterned RSLSC isilluminated uniformly over an increasingly larger area, whichcorresponds directly to increasing the geometric gain G=x/t, where t isthe substrate 12 thickness. The RSLSCs are patterned with a repeating6-level stair step pattern, with step widths and heights of 2 mm and 30nm, respectively.

FIG. 5 b shows that the RSLSC with an F8BT emissive layer outperformsits LSC 10 counterpart, delivering more luminescence to the edge-mountedphotodiode 20 despite absorbing less of the incident light on average(lower panel). The result is similar for L305 in FIG. 5 c, where theRSLSC and LSC 10 control have nearly identical absorption, yet the RSLSCmoves from delivering less power at small G to more power at large G.The ratio of RSLSC to LSC 10 output power thus increases with geometricgain. This increase can only be explained by lower overall propagationloss in the RSLSC since it is the only factor that depends on G. FIG. 5d summarizes this ratio for all of the emitters on both borosilicate andhigh-index SF10 glass. The increasing trend evident in every caseconfirms that resonance-shifting is a highly robust method of reducingreabsorption loss in luminescent concentrators. The opposite trend isobserved in control experiments comparing conventional LSCs 10 withdiffering dem, where, as expected, the delivered power ratio of thick tothin devices decreases with increasing G due to higher loss in thethicker films.

FIG. 6 a extends the L305 simulation in FIGS. 4 c and 4 d to model thearea excitation experiment, where for simplicity, an ideally patternedRSLSC is used in which emission from a given point never re-encountersits own reflectivity resonance. The model reproduces the trend in powerratio observed in the data of FIG. 5 d, predicting the same ˜10%enhancement at G=50 realized by resonance-shifting. However, accountingfor emission from the other three edges and extending the samesimulation to larger geometric gain in FIG. 6 b shows that theimprovement grows markedly with increasing concentrator size due to theamplified benefit of loss reduction. Indeed, whereas the LSC 10concentration ratio saturates at CR˜10 (ηopt=2%), that of the RSLSCreaches CR=24 (ηopt=4.8%) at G=500, reflecting a 2.4× increase that isstill growing. Here, the use of an external back reflector is assumed todouble the absorption path length of sunlight through the L305 film(ηabs=0.26, ηStokes=0.73) and that the photoluminescent quantum yield isincreased to 98% as it is when L305 is dispersed in a host matrix.Because the improvement in concentration ratio hinges entirely onreduced RSLSC propagation loss, there may be even greater relativebenefit for single-sided collection when the other edges are silvereddue to the overall increase in path length to the solar cell.

For certain embodiments, the stair step thickness variation 18 used inFIG. 5 may not be the optimum way to pattern an RSLSC. As emission fromeach resonance has a different return-length to the luminescent film 16depending on its emission angle and the substrate 12 thickness, RSLSCspresent a complex optimization challenge that will likely require raytracing in combination with thin-film optical modeling to determine theemission pattern, efficiency, and reflectivity at each point on thesurface, for each wavelength in the emission spectrum. The goal is todetermine how best to pattern lateral variation 18 in the luminescentfilm 16 thickness to maximize the non-resonant path length of emissionfrom each point to the collecting edge(s) subject to a finite number ofavailable resonances, since emission originating from, e.g. a TE1 modethat encounters a TE2 reflectivity resonance at the same angle willexperience loss.

The number of non-overlapping resonances is determined by the angularwidth of each, which in turn depends on the low-n layer thickness aswell as the extinction coefficient of the luminescent film 16. Theresonances cannot be made arbitrarily narrow since the associatedincrease in cavity Q-factor leads to more initial reabsorption loss,reducing the quantum yield of emission into the substrate 12. Thesubstrate-coupled quantum yield of the cavity structure thus depends ondlow. It can usually be made comparable to or greater than that of thecorresponding non-cavity, though in general, the optimum low-n layerthickness decreases as the substrate 12 refractive index increases. InFIG. 5 d, all of the cavities share dlow=230 nm, and hence the powerratios for the SF10-based cavities are lower than their glasscounterparts.

Resonance-shifting is most effective for thin luminescent films 16, lessthan ˜1 μm thick that support only one or two modes of eachpolarization, since highly multimode films make it difficult to avoidoverlapping resonances. Dense, strongly absorbing films of organicchromophores or colloidal quantum dots with absorption lengths of a fewhundred nanometers are thus well suited for this approach. Althoughquenched in neat film here, the photoluminescent quantum yield of theLumogen dyes can be greatly increased by doping into a host matrix,though it should be noted that similar red perylene dyes exhibiting highquantum yield in neat film have also been developed. Colloidal quantumdots, in many respects ideal for use in LSCs 10 due to their broadabsorption and tunable emission, may especially benefit from theresonance-shifting approach, as their use to date has been particularlyhampered by high reabsorption losses.

Ultimately, RSLSCs retain the potential for low-cost fabrication, takingadvantage of solution processable low-index and luminescent layers 16 aswell as additive stamp-transfer processes to pattern the thicknessvariation 18 in a roll-to-roll fashion. One of ordinary skill in the artwill appreciate that the present invention need not be limited by themechanism utilized to achieve resonance shifting and other ways ofachieving resonance-shifting are contemplated. For example, theluminescent film 16 thickness need not be varied at all if a substrate12 with a shallow, slowly varying lower surface profile are used (e.g.reflecting light back at slightly different angles), though this couldlead to unacceptable out-coupling loss from rays returned below thecritical angle. Another way to achieve resonance-shifting is tolaterally vary the refractive index gradient in the substrate 12. Stillanother way to achieve resonance-shifting is to use a curved substrate12 (e.g. a glass plate deformed into a demisphere, parabloid, or thelike), with a luminescent thin film 10 disposed on one side. One skilledin the art will appreciate that other mechanisms for achieving resonanceshifting may be employed without deviating form the spirit of thisdisclosure.

Example Sample Fabrication, Measurement and Data Analysis

Borosilicate glass microscope slides (60 mm×25.4 mm×1 mm, Fischer) andpolished pieces of SF10 glass (58 mm×25.4 mm×1.15 mm, VPG optical glass)were used as substrates 12. Low refractive index layers were fabricatedusing the sacrificial porogen method as detailed previously, whichproduces uniform optical quality films with RMS surface roughness <2 nmand a nearly dispersionless refractive index of nlow˜1.14. Films of F8BTwere first spin-coated from p-xylene on a water-soluble sacrificiallayer and then float-transferred onto the nanoporous low index spacerlayer to produce a well-defined interface. The L170 and L305 cavitieswere produced by thermally evaporating the dyes directly onto the low-nlayer. Optical constants and layer thicknesses were determined fromglobal fitting of variable-angle spectroscopic ellipsometry and normalincidence transmission measurements.

Resonance-shifted stripe regions in the F8BT cavities were produced bythermally evaporating Alq3 through a shadow mask, whereas additionalL170 and L305 was deposited in the case of the Lumogen cavities. Thestair-step pattern of the full RSLSCs was built up sequentially usingthe appropriate series of shadow masks and was simultaneously depositedon the LSC 10 control devices (which have no low-n layer) to maintaincomparable absorption to the RSLSCs.

Cavity reflectivities were collected as a function of angle via anequilateral prism index-matched to the back of each substrate 12 usingλ=543 nm and λ=635 nm lasers for the F8BT and Lumogen-based cavities,respectively. Angular emission patterns of the F8BT cavity on glass wereobtained exciting at λ=473 nm, out-coupling with an index-matchedhalf-ball lens and detecting with an angular resolution of 0.1 degrees.Both reflectivity and emission signals were chopped at 300 Hz anddetected with a Si photodiode 20 and lock-in amplifier.

Luminescence was detected from the concentrator edge by attachingdirectly to the surface of a bare, rectangular Si photodiode 20 (5mm×25.4 mm, Silonex) with index-matching fluid (n=1.52 for glass, n=1.72for SF10, Cargille Labs) to prevent any air gaps. The remaining threeedges were blackened with ink to minimize edge reflections, whichcomplicate the modeling analysis. Laser excitation (λ=473 nm for F8BTand L170, λ=543 nm for L305) was chopped at 300 Hz and directed onto thecavity surface approximately 5 degrees from normal incidence. The focalpoint (˜200 μm diameter) was scanned as a function of position, x, alongthe middle of each sample while synchronously collecting the edgeluminescence, transmitted, and reflected beam intensities at each point.The optical internal quantum efficiency was calculated using these dataand then corrected for the solid angle change multiplying by π/2tan⁻¹(w/2x) as previously, where w is the length of the edge with theattached photodiode 20. This correction is not valid for small x on theorder of the 1 mm substrate 12 thickness and hence the propagationefficiency, ηprop (x), was estimated relative to the point x=5 mmthrough the relationship IQE(x)=η_(em)η_(prop)(x) for the LSC 10control, since the emission quantum yield, ηem, is constant throughout.The emission quantum yield is not constant crossing over theresonance-shifted stripe region of the cavities and so in this case thepropagation efficiency is derived by geometrically averaging thecomplementary cavity data to deconvolve changes in ηem according to thefollowing:

√{square root over (IQE_(RS−)(x)IQE_(RS+)(x))}{square root over(IQE_(RS−)(x)IQE_(RS+)(x))}=η_(prop,avg)(x)√{square root over(η_(em+)η_(em−))}

Edge-emission spectra were collected through the port of an integratingsphere that was fiber-coupled to a cooled Si CCD spectrograph.

Broad area illumination with an intensity of approximately 30 mW/cm2,chopped at 300 Hz and incident normal to the sample, was provided by aquartz-tungsten-halogen lamp homogenized using a tapered light pipe toachieve spatial uniformity with <1% r.m.s. intensity variation. Thephotodiode 20 was attached and the other edges blackened as above, witha small cover used to prevent direct illumination of the photodiode 20.The lamp output was subsequently shortpass filtered below λ=500 nm tominimize noise from scattered near-infrared light not absorbed by theluminescent film layers 16, and testing of blank samples (e.g. plainglass) ensured that stray light remained negligible in comparison to theluminescence signal.

Anisotropic transfer matrix modeling was used to fit the angularreflectivity data for the F8BT cavities since these films are uniaxial,with ordinary and extraordinary refractive indices no=1.70 and ne=1.65,and isotropic extinction k=1.5×10−4 at λ=543 nm as previously. The modelfits for the F8BT cavity in FIG. 2 b are reproduced in FIG. 8 a (TEpolarization) and 8 b (TM polarization), excluding prism-couplingreflections to show the true internal reflectivity of the cavity. Theplots with circles denote reflectivity of the F8BT cavity and the plotswith squares show reflectivity of the F8BT control, where the same filmlies directly on the glass substrate 12. Deviation from unity indicatesreabsorption since no light is transmitted beyond the critical angle(˜42°). It is clear that loss is much lower for non-resonant cavityangles than it is across all angles for the film on glass.

Dashed arrows in FIGS. 8 a and 8 b indicate the peak position ofemission from the resonance-shifted stripe in FIG. 3. At these angles,emission is subject to 6- and 12-fold reductions in reabsorption at eachreflection as compared to the control film for TE and TM polarizationsrespectively. FIGS. 8 c and 8 d show the intensity profiles (|Ey|2 forTE and |Hy|2 for TM polarizations) that correspond to these particularangles, demonstrating the suppression of fields in the F8BT film thatoccurs off resonance. Averaged over all non-resonant angles,reabsorption loss for the cavity is a factor of 38× and 15× lower thanthe control film for TE and TM polarized emission, respectively.

Global fits of variable angle spectroscopic ellipsometry and normalincidence transmission data are used to extract the optical constants ofeach film for modeling. Since this procedure is not sensitive to theweak extinction present below the absorption edge of each material,extinction coefficients determined from the resonant reflectivityfitting (λ=543 nm for F8BT, λ=635 nm for L170 and L305) are used as datapoints to fix the magnitude at these wavelengths and then extrapolatethe functional decay determined by ellipsometry.

Total dipolar radiated and dissipated (into the lossy luminescent film16) power, was calculated for the cavities numerically using the methodof source terms, assuming randomly oriented dipoles distributedthroughout the emissive layer and excited in proportion to the amount ofincident light absorbed at each position. From this the total power isobtained for each polarization emitted into the substrate 12 as afunction of angle for each wavelength in the emission spectrum,normalized to the calculated substrate-coupled emission quantum yield:

η_(em)(λ)=2π∫[I _(TE)(θ,λ)+I _(TM)(θ,λ)] sin(θ)dθ,  [Equation 1]

where θ is the angle in the substrate 12 and ITE and ITM are the TE andTM polarized power patterns, respectively. Using the transfermatrix-calculated reflectivities, RTE(0,λ) and RTM(θ,λ), the respectivepropagation losses in the {circumflex over (x)} direction for eachemitted angle according to the geometry illustrated in FIG. 9 is asfollows:

$\begin{matrix}{{\alpha_{TE}\left( {\theta,\varphi,\lambda} \right)} = {{\frac{- {\ln \left( R_{TE} \right)}}{2{t\left( {\tan \mspace{11mu} \theta \mspace{11mu} \cos \mspace{11mu} \varphi} \right)}}\mspace{14mu} {and}\mspace{14mu} {\alpha_{TM}\left( {\theta,\varphi,\lambda} \right)}} = {\frac{- {\ln \left( R_{TM} \right)}}{2{t\left( {\tan \mspace{11mu} \theta \mspace{11mu} \cos \mspace{11mu} \varphi} \right)}}.}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

The power reaching the photodiode 20 at the right-hand edge (see FIG. 9)from a given location (x,y) at wavelength, λ, is then given byintegrating over solid angle:

I(x,y,λ)=∫_(φ) _(L) ^(φ) ^(U) ∫₀ ^(π/2) [I _(TE)exp(−α_(TE) x)+I_(TM)exp(−α_(TM) x)] sin θdθdφ,  [Equation 3]

where the azimuthal angular limits are:

$\begin{matrix}{\varphi_{L} = {{{\tan^{- 1}\left\lbrack \frac{{w\text{/}2} + y}{x} \right\rbrack}\mspace{14mu} {and}\mspace{14mu} \varphi_{U}} = {{\tan^{- 1}\left\lbrack \frac{{w\text{/}2} - y}{x} \right\rbrack}.}}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

Integrating Equation 3 over the normalized photoluminescence spectrumgives the total power arriving from each position. Secondary re-emissionevents (e.g. emission following reabsorption) are neglected and lightscattered from the other edges are not accounted for since this isminimized by edge blackening in our experiments. Further integration ofEquation 3 over x and y gives the edge-intensity under areaillumination. Symmetry considerations and the appropriate change ofvariables in Equation 3 enable the calculation of light from all edges.

The simulation of ideally patterned RSLSCs in FIG. 6 assumes thatemission from a given point never re-encounters its own reflectivityresonance. As the optimum pattern is not yet known, this condition isartificially enforced in the simulation by ensuring that the layerthickness for each emitting point is always different than the rest ofthe structure (i.e. if light is emitted from a point with layerthickness dem, then the rest of the surface has layer thickness dem+30nm).

The foregoing description of embodiments of the present invention havebeen presented for purposes of illustration and description. It is notintended to be exhaustive or to limit the present invention to theprecise form disclosed, and modifications and variations are possible inlight of the above teachings or may be acquired from practice of thepresent invention. The embodiments were chosen and described in order toexplain the principles of the present invention and its practicalapplication to enable one skilled in the art to utilize the presentinvention in various embodiments, and with various modifications, as aresuited to the particular use contemplated.

What is claimed is:
 1. A method for increasing the efficiency of aluminescent solar concentrator, comprising: providing a transparentsubstrate; providing a low refractive index layer to a surface of thetransparent substrate; and providing a luminescent film of laterallyvarying thickness, the laterally varying thickness defining a firstthickness at a first location and a second thickness at a secondlocation, such that the low refractive index layer is disposed betweenthe transparent substrate and the luminescent film.
 2. The method ofclaim 1, wherein the luminescent film is deposited onto a transfermedium by spin coating and is transferred to the luminescent solarconcentrator by float transfer.
 3. The method of claim 1, wherein thevariable thickness of the luminescent film is provided by depositingvariable amounts of luminescent film onto the transfer medium.
 4. Themethod of claim 1, wherein the low refractive index layer has arefractive index of about 1.1 to about 1.2.
 5. The method of claim 4,wherein the low refractive index layer has a refractive index of about1.14.
 6. The method of claim 1, wherein the first location is spacedfrom the second location such that resonant emission from either rof thefirst and the second locations of the luminescent film does notre-encounter that same resonance in reflectivity.
 7. The method of claim1, evanescently coupling the luminescent film to the transparentsubstrate.
 8. The method of claim 1 wherein the luminescent filmcomprises a thickness of one micron or less and the lateral varyingthickness of the luminescent film comprises a step-wise thicknessvariation.
 9. The method of claim 1, further comprising emitting lightthrough the luminescent film at a first position, then transmittedwithin the transparent substrate, and is reflected off the luminescentfilm at a second position, wherein the luminescent film thickness at thefirst position being different than the thickness at the secondposition.
 10. A method for directing light, comprising: absorbing alight at a first location in a luminescent film; emitting the lightthrough a low refractive index layer into a transparent substrate, theemitted light evanescently coupled into the transparent substrate;reflecting the light from a bottom boundary of the transparentsubstrate; reflecting the light from a second location in theluminescent film laterally displaced from the first location, whereinthe light exhibits non-resonant near-unity reflectivity.
 11. The methodof claim 10, further comprising directing the light from the firstlocation in the luminescent film to the second location by varying thethickness of the luminescent film.
 12. The method of claim 10, furthercomprising directing the light from the first location in theluminescent film having a first thickness to the second location havinga second thickness.
 13. The method of claim 12, wherein the luminescentfilm comprises a thickness of one micron or less and the lateral varyingthickness of the luminescent film comprises a step-wise thicknessvariation.
 14. The method of claim 12, further comprising evanescentlycoupling the luminescent film to the transparent substrate.
 15. Themethod of claim 10, further comprising directing the light from thefirst location in the luminescent film to the second location byinteracting the light with the transparent substrate having a laterallyvarying the refractive index.
 16. The method of claim 10, furthercomprising directing the light from the first location in theluminescent film to the second location by deforming the transparentsubstrate such that the substrate is curved.
 17. The method of claim 10,wherein the light reflecting from the second position is off-resonancefrom the light absorbed through the first position.